Qualitative Analysis Of Functional Differential Systems And Its Applications In Neural Networks

This paper is concerned with the qualitative analysis of functional differentialsystems and stochastic functional differential systems, such as dissipativity, periodicsolutions, invariant set and attractivity, and its Applications in neural networks.Chapter 1 offers the research background for this paper, and some known re-suits for the qualitative analysis of deterministic functional differential equations andstochastic functional differential equations are introduced.In Chapter 2, the existence theorem for periodic Markov process is firstly de-veloped by employing the properties of transition functions and Markov inequality.Furthermore, the existence theorem for periodic solution of It(?) stochastic functionaldifferential equations is given. Lastly, by using stochastic analysis technique and It(?)formula, sufficient conditions for the existence of invariant set, attracting set and peri-odic attractor for stochastic neural networks with delays are obtained.In Chapter 3, a class of neural networks with mixed delays is considered. Theexistence, uniqueness and global asymptotic stability of the equilibrium for the neuralnetworks are established by means of Leray-Schauder principle, Arithmetic-mean-geometric-mean inequality and a vector delay differential inequality.In Chapter 4, the dissipativity and periodic attractor of a class of non-autonomousneural networks with time-varying delays are investigated. Firstly, by employing theproperties of M-matrix and a delayed differential inequality, the uniformly dissipativ-ity of the neural networks is obtained. Then, by using the Banach fixed point theory, the sufficient conditions for the existence and uniqueness of the periodic solutions ofa class of nonlinear functional differential equations are given. Lastly, some sufficientconditions for the existence range of the periodic attractor are obtained by using theabove results.In Chapter 5, a class of fuzzy neural networks with delays is considered. Byemploying the properties of M-matrix and the techniques of inequality, dissipativity,invariant sets and attracting sets of the system are obtained.